On the other hand, we can observe that for \(5<\textrm {K}\le 65\) , \((\Delta f_{K})_{\mathrm {adj}}\)  is monotonically decreasing, and for \(\textrm {K}>65\)  it is again monotonically increasing.
We can also observe that, between \(K>0\)  and \(K\doteq 80\) , \((\Delta f_{K})_{\mathrm {rnd}}<(\Delta f_{K})_{\mathrm {adj}}\) .
Contrary to the case of random epistatic interactions, for adjacent interactions \((\Delta f_{K})_{\mathrm {adj}}\)  is higher since the fitness values reached by inversions are higher than those reached by point mutations (note in Fig REF  the gap between the red and blue curves with the marker `+').
So, we infer that an inversion—modifying several loci—results in a mutually advantageous conjunction with local epistatic interactions, that allows explorations of more combinations that can be beneficial.
Finally, for \(K>80\) , \((\Delta f_{K})_{\mathrm {rnd}}\approx (\Delta f_{K})_{\mathrm {adj}}\)  (still monotonically increasing), i.e. regardless of the epistatic interaction neighbourhood,
inversions can reach higher fitness values and attenuate the complexity catastrophe by not decreasing towards \(1/2\)  (compare with [1]} and also note in Fig REF , the gap between the tails of the red and blue curves).
